Package dk.jonaslindstrom.ruffini.quadraticform

Class ClassGroup

java.lang.Object

dk.jonaslindstrom.ruffini.quadraticform.ClassGroup

All Implemented Interfaces:

Group<QuadraticForm<BigInteger,BigIntegers>>, Monoid<QuadraticForm<BigInteger,BigIntegers>>, Semigroup<QuadraticForm<BigInteger,BigIntegers>>, Set<QuadraticForm<BigInteger,BigIntegers>>

public class ClassGroup
extends Object
implements Group<QuadraticForm<BigInteger,BigIntegers>>

This implements the ideal class group for a negative discriminant.

Constructor Summary

Constructors

Constructor	Description
ClassGroup(BigInteger discriminant)

Method Summary

Modifier and Type	Method	Description
boolean	equals(QuadraticForm<BigInteger,BigIntegers> a, QuadraticForm<BigInteger,BigIntegers> b)	Returns true if and only if a = b as elements of this set.
QuadraticForm<BigInteger,BigIntegers>	identity()	Return the identity element of this monoid.
QuadraticForm<BigInteger,BigIntegers>	invert(QuadraticForm<BigInteger,BigIntegers> a)	Return the inverse a-1.
QuadraticForm<BigInteger,BigIntegers>	multiply(QuadraticForm<BigInteger,BigIntegers> a, QuadraticForm<BigInteger,BigIntegers> b)	Return the result of the product ab in this group.
QuadraticForm<BigInteger,BigIntegers>	sample(Random random)
String	toString(QuadraticForm<BigInteger,BigIntegers> a)	Returns a human-readable string representation of an element in this set.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Group

divide

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Monoid

isIdentity, power

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Semigroup

multiply, multiply

Constructor Details

ClassGroup

public ClassGroup(BigInteger discriminant)

Method Details

invert

public QuadraticForm<BigInteger,BigIntegers> invert(QuadraticForm<BigInteger,BigIntegers> a)

Description copied from interface: Group

Return the inverse a^-1.

Specified by:

invert in interface Group<QuadraticForm<BigInteger,BigIntegers>>

identity

public QuadraticForm<BigInteger,BigIntegers> identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<QuadraticForm<BigInteger,BigIntegers>>

multiply

public QuadraticForm<BigInteger,BigIntegers> multiply(QuadraticForm<BigInteger,BigIntegers> a,
 QuadraticForm<BigInteger,BigIntegers> b)

Description copied from interface: Semigroup

Return the result of the product ab in this group.

Specified by:

multiply in interface Semigroup<QuadraticForm<BigInteger,BigIntegers>>

toString

public String toString(QuadraticForm<BigInteger,BigIntegers> a)

Description copied from interface: Set

Returns a human-readable string representation of an element in this set.

Specified by:

toString in interface Set<QuadraticForm<BigInteger,BigIntegers>>

equals

public boolean equals(QuadraticForm<BigInteger,BigIntegers> a,
 QuadraticForm<BigInteger,BigIntegers> b)

Description copied from interface: Set

Returns true if and only if a = b as elements of this set.

Specified by:

equals in interface Set<QuadraticForm<BigInteger,BigIntegers>>

sample

public QuadraticForm<BigInteger,BigIntegers> sample(Random random)